Problem: Which of the following numbers is a multiple of 10? ${45,64,66,78,90}$
Explanation: The multiples of $10$ are $10$ $20$ $30$ $40$ ..... In general, any number that leaves no remainder when divided by $10$ is considered a multiple of $10$ We can start by dividing each of our answer choices by $10$ $45 \div 10 = 4\text{ R }5$ $64 \div 10 = 6\text{ R }4$ $66 \div 10 = 6\text{ R }6$ $78 \div 10 = 7\text{ R }8$ $90 \div 10 = 9$ The only answer choice that leaves no remainder after the division is $90$ $ 9$ $10$ $90$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $10$ are contained within the prime factors of $90$ $90 = 2\times3\times3\times5 10 = 2\times5$ Therefore the only multiple of $10$ out of our choices is $90$. We can say that $90$ is divisible by $10$.